randRange( 1, 14 ) randRange( NUM_1 + 1, 15 ) NUM_1 randRange( NUM_2 + 1, 15 ) (function() { if ( DEN_1 < DEN_2 ) { return ">"; } else { return "<"; } })() DEN_1 > DEN_2 ? "more" : "fewer" DEN_1 > DEN_2 ? "smaller" : "bigger" DEN_1 > DEN_2 ? "less" : "more" SMALLER === "smaller" ? "bigger" : "smaller"

Fill in the blank.

\dfrac{NUM_1}{DEN_1} ____ \dfrac{NUM_2}{DEN_2}

SOLUTION

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This is like comparing two equally sized pizzas where one is cut into DEN_1 equal slices and the other is cut into DEN_2 equal slices.

init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_1, DEN_1 - NUM_1], ["#e00", "#999"], 2 );
init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_2, DEN_2 - NUM_2], ["#e00", "#999"], 2 );

Note that cutting a pizza into more slices will result in smaller slices.

The left fraction represents a pizza with MORE slices, and so each slice is SMALLER.

NUM_1 SMALLER sliceplural( NUM_1 ) is LESS pizza than NUM_2 BIGGER sliceplural( NUM_2 ).

So, \dfrac{NUM_1}{DEN_1} SOLUTION \dfrac{NUM_2}{DEN_2}.

randRange( 1, 14 ) randRange( NUM_1 + 1, 15 ) DEN_1 randRange( 1, DEN_2 - 1 ) (function() { if ( NUM_1 < NUM_2 ) { return "<"; } else { return ">"; } })() NUM_1 < NUM_2 ? "less" : "more"

Fill in the blank.

\dfrac{NUM_1}{DEN_1} ____ \dfrac{NUM_2}{DEN_2}

SOLUTION

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This is like considering two equally sized pizzas that have been cut into DEN_1 equal slices.

Since both pizzas have the same number of slices, all the slices are the same size.

init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_1, DEN_1 - NUM_1], ["#e00", "#999"], 2 );
init({ range: [ [-3, 3], [-3, 3] ], scale: 25 }); piechart( [NUM_2, DEN_2 - NUM_2], ["#e00", "#999"], 2 );

plural( NUM_1, "slice" ) is LESS pizza than plural( NUM_2, "slice" ).

So, \dfrac{NUM_1}{DEN_1} SOLUTION \dfrac{NUM_2}{DEN_2}.